Math Question 6: Consider a non-dividend-paying stock whose current price is $100. A market maker writes a one-year call option on this stock and sells it for $4.00. He then proceeds to delta-hedge his commitment by trading in the shares of the underlying stock. The call option’s delta is 0.75, its gamma is 0.08 and its theta is−0.02 per day. The continuously compounded, risk-free interest rate is 4%. The stock price has risen to $101 after one day. Use the delta-gamma-theta approximation to find the change in market maker’s portfolio after one day.Enter your answer in cents (NOT dollars) rounded to two decimal places.

Math Question 2: Assume Black-Scholes framework. Given a non-dividend stock with current price $70 and volatility 30% per annum. The continuously compounded risk free rate is 8% per annum. Consider a European call option with expiry time 1 year and strike price $75. What is the price of a knock-out call with a barrier of $74 (in dollars)?

Math Question 8: Consider three risky securities with expected returns µ1 = 0.08, µ2 = 0.10, µ3 = 0.16 and with the covariance matrix and its inverse given by Screenshot 2025-05-05 at 1.24.45 PM.png (a) Find the weights of the minimum variance portfolio with these three securities. (b) Does this portfolio involve short-selling? Answer each part of the question above on paper. Once completed, select “True” below.

Place the levels of measurement in order from least to most information. Hint: Remember, only the highest two levels involve numbers you can do meaningful math with.

Question: The stem-and-leaf plot below shows the ages of patients seen during one day in a clinic. Stem | Leaf 2 | 3 4 5 8 3 | 0 1 1 2 4 | 2 4 6 9 5 | 1 3 How many patients are 30 years old or older?  

Steles are:

Children’s physical development

Affective development with social understanding may offer children opportunities to 

An integrated curriculum plan in an early care and learning program

In class we discussed the paper, “Optogenetics enables functional analysis of human embryonic stem cell-derived grafts in a Parkinson’s disease model”. The figures below come from that paper. (FYI: Halorhodopsin-EYFP is the same thing as eNpHR3.0-EYFP) Match each panel (A, B, and C) with the mouse genotype that could be responsible for the data.